Arctangent (atan) Calculator
Find the angle whose tangent is a given value. You can enter a direct ratio x, or compute it from opposite/adjacent sides.
What is atan?
atan (also written as arctan or inverse tangent) is the inverse function of tangent. If tan(θ) = x, then atan(x) = θ. In other words, it gives you the angle when you already know a tangent ratio.
The output from an atan calculator is usually shown in both radians and degrees.
Most coding and math libraries return radians by default, including JavaScript's Math.atan().
How to use this atan calculator
Method 1: Direct ratio
- Enter a value in Tangent value x.
- Click Calculate atan.
- Read your angle in radians and degrees.
Method 2: Triangle sides
- Enter Opposite and Adjacent side lengths.
- The calculator computes x = opposite / adjacent.
- Then it calculates atan(x).
Worked examples
Example 1: atan(1)
Because tangent of 45° is 1, atan(1) = 45° = π/4 radians. This is one of the most common checks for an inverse tangent calculator.
Example 2: atan(0.57735)
Since tan(30°) ≈ 0.57735, the result is about 30° (or 0.523599 radians).
Example 3: opposite = 8, adjacent = 4
Ratio x = 8/4 = 2. Then atan(2) ≈ 63.4349°. This is useful in slope and incline calculations.
Radians vs degrees
Both are valid angle units. Degrees are more intuitive for everyday use; radians are standard in calculus, physics, and programming.
| Tangent value x | atan(x) in radians | atan(x) in degrees |
|---|---|---|
| -1 | -0.785398 | -45° |
| 0 | 0 | 0° |
| 1 | 0.785398 | 45° |
Where an arctan calculator is used
- Geometry: finding unknown angles in right triangles.
- Engineering: slope, grade, and direction calculations.
- Physics: vector direction from component values.
- Computer graphics: camera rotation and orientation math.
- Data science: angle transformations and trigonometric modeling.
Common mistakes to avoid
- Mixing up tan and atan.
- Forgetting whether your answer is in radians or degrees.
- Using adjacent = 0 when computing a ratio from side lengths.
- Rounding too early in multi-step calculations.
Final notes
A reliable atan calculator should be quick, precise, and clear about units. Use this tool when you need inverse tangent, arctan in degrees, arctan in radians, or triangle-angle solving from side ratios. For quadrant-aware directional angles from y and x, use atan2 instead of plain atan.